It is known that the angle BCD in the triangle BCD is 90 degrees BC=CD= 1 AB perpendicular to the plane BCD, and the angle ADB=60 degrees E F is the moving point on AC AC and AE/AC = AF/AD = λ (0 < λ < 1) respectively.

Verify that 1 No matter what the value of λ is, there is always a straight line EF// plane DBC.

When λ is what value, the plane BEF is perpendicular to the plane ACD.

The intersection of AE and BC in extension F.

∠EAD=∠CBD

∠ACF =∠ACB = 90°

AC=BC

δACF?δBCD

∴AF=BD

AE= 1/2BD

∴EF= 1/2BD=AE

δ Abbe δ FBE

∴∠ABD=∠CBD